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arxiv: 2509.09986 · v3 · submitted 2025-09-12 · 🌀 gr-qc · hep-ph· hep-th

Plunge spectra as discriminators of black hole mimickers

Sreejith Nair This is my paper

Pith reviewed 2026-05-18 18:12 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-th
keywords black hole mimickersplunge spectraquasi-normal modesgravitational wavesextreme mass ratio inspiralsspectral resonancesblack hole discrimination
0
0 comments X p. Extension

The pith

Plunge spectra produce resonance combs and a high-frequency break that set black hole mimickers apart from black holes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether the plunge phase of an extreme mass ratio inspiral can serve as a discriminator for black hole mimickers. It establishes that the plunge generically excites a low-frequency comb of sharp resonances located at the real parts of the mimicker quasi-normal modes. Above a threshold frequency Mω_th ≈ 0.39 for the dominant mode, the spectrum exhibits a qualitative break with substantial deviations from black hole behavior. These coherent features offer a route to boost signal-to-noise ratio by stacking multiple events even when single-event signals remain weak against noise.

Core claim

The plunge excites two generic spectral features. At low frequencies there is a comb of sharp resonances at the real parts of the mimicker quasi-normal modes. Above a threshold Mω_th ≈ 0.39 for the dominant mode the spectrum undergoes a qualitative break, with the black hole mimicker displaying significant deviations from the black hole.

What carries the argument

The plunge spectrum, the frequency content of the gravitational-wave signal during the rapid infall phase, which carries the excitation of quasi-normal modes as observable resonances and a spectral break.

If this is right

  • The two spectral features arise generically for a broad class of black hole mimickers.
  • Low-frequency resonances directly encode the real parts of the mimicker quasi-normal modes.
  • The qualitative break above Mω_th ≈ 0.39 produces clear deviations from black hole plunge spectra.
  • Coherent stacking of multiple low-SNR events can enhance detectability of the shared spectral signatures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future space-based detectors sensitive to extreme mass ratio events could search for these resonance combs to constrain the presence of horizonless objects.
  • The frequency threshold provides a concrete target band for narrow-band filtering or template matching in data analysis.
  • If the features hold, they would complement existing tests based on ringdown or shadow observations by probing the plunge regime directly.

Load-bearing premise

The plunge dynamics and quasi-normal mode excitations produce these spectral features generically across a broad class of mimickers independent of their specific internal structure.

What would settle it

Plunge spectra extracted from extreme mass ratio inspirals that show neither the low-frequency resonance comb nor the break above Mω ≈ 0.39 would falsify the claim that these features generically discriminate mimickers.

Figures

Figures reproduced from arXiv: 2509.09986 by Sreejith Nair.

Figure 1
Figure 1. Figure 1: Plot of dE/µ2 dω versus Mω for the (ℓ, m) = (2, 2) modes of the GW perturbations for a black-hole mimicker with a reflecting surface at rs = 2M(1 + ϵ), ϵ = 10−10 from a radial plunge. Here µ is the mass of the point particle falling inwards. The black and brown vertical lines mark the Schwarzschild fundamental QNM frequency BHωQNM and ωth. As expected we see a qualitative change above Mωth ≳ 0.39 which cor… view at source ↗
Figure 2
Figure 2. Figure 2: Plot of dE/µ2 dω against Mω for the (ℓ, m) = (2, 2) modes of the GW perturbations for a black hole mimicker with a reflecting surface at rs = 2M(1 + ϵ) from a radial plunge.. Here µ is the mass of the point particle falling inwards. We have set R = 1 on the reflecting surface and have varied the separation of the reflecting surface (ϵ) from the supposed horizon of the black hole mimicker. It can be seen th… view at source ↗
Figure 3
Figure 3. Figure 3: Plot of dE/µ2 dω against Mω for the (ℓ, m) = (2, 2) modes of the GW perturbations for a black hole mimicker with a reflecting surface at rs = 2M(1 + ϵ), ϵ = 10−4 . We have presented the energy spectrum for point particles with different angular momentum plunging into the black hole mimicker. Different values of L are represented as varying shades of green, with the corresponding black hole case being repre… view at source ↗
read the original abstract

This work explores the prospect of using the plunge to identify potential black hole mimickers. We show that the plunge excites two generic spectral features. (i) At low frequencies, there is a comb of sharp resonances at the real parts of the mimicker quasi-normal modes. (ii) Above a threshold $M\omega_{\rm th}\!\approx\!0.39$ (for the dominant mode), the spectrum undergoes a qualitative break: with the black hole mimicker displaying significant deviations from the black hole. Though individual plunge SNRs in extreme mass ratio events are low and detecting them in a sea of noise is difficult, the coherent spectral features identified here may allow for enhancing the SNR by using multiple events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript explores the prospect of using plunge signals in extreme mass ratio systems to discriminate black hole mimickers from true black holes. It claims that the plunge excites two generic spectral features: (i) at low frequencies, a comb of sharp resonances at the real parts of the mimicker quasi-normal modes, and (ii) above a threshold Mω_th≈0.39 (for the dominant mode), a qualitative break in the spectrum with significant deviations from the black hole case. The coherent use of spectral features across multiple low-SNR events is proposed to enhance detectability.

Significance. If the claimed features prove generic and independent of specific mimicker interiors, the work offers a potentially useful observational handle on the nature of compact objects via gravitational-wave plunge spectra. The emphasis on coherent stacking to mitigate low individual SNRs is a practical positive. However, the absence of explicit derivations or cross-model validations in the presented material limits the immediate impact.

major comments (2)
  1. Abstract: The threshold Mω_th≈0.39 is asserted as the location of a qualitative spectral break without derivation, model equations, error bars, or validation data. This is load-bearing for the central claim of a generic discriminator, as it is unclear whether the break arises independently of the mimicker assumptions or is tied to the same interior model used to define the resonances.
  2. Abstract (genericity paragraph): The claim that both the low-frequency QNM comb and the spectral break arise for a broad class of mimickers independent of internal structure details is stated but not demonstrated. No explicit comparison across different boundary conditions (e.g., perfectly reflecting surface vs. finite-thickness shell) or effective potentials is referenced, which directly affects whether the discriminator is model-independent as asserted.
minor comments (1)
  1. Abstract: The notation for the threshold frequency could include a brief parenthetical definition or reference to the dominant mode to improve standalone readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive feedback. We appreciate the recognition of the potential utility of plunge spectra for discriminating black hole mimickers and address each major comment point by point below.

read point-by-point responses

  1. Referee: Abstract: The threshold Mω_th≈0.39 is asserted as the location of a qualitative spectral break without derivation, model equations, error bars, or validation data. This is load-bearing for the central claim of a generic discriminator, as it is unclear whether the break arises independently of the mimicker assumptions or is tied to the same interior model used to define the resonances.

    Authors: We thank the referee for this observation. The threshold Mω_th ≈ 0.39 is obtained from the explicit computation of the plunge waveform spectrum in the main text, where the Fourier transform of the signal for the mimicker is compared directly to the black hole case. It corresponds to the frequency scale above which the reflective boundary condition at the mimicker surface produces a clear deviation in the high-frequency content. While the abstract presents this as a summary statement, we agree that additional context would improve clarity. We have revised the abstract to briefly indicate that the threshold is identified through the spectral analysis and is associated with the dominant mode. revision: yes

  2. Referee: Abstract (genericity paragraph): The claim that both the low-frequency QNM comb and the spectral break arise for a broad class of mimickers independent of internal structure details is stated but not demonstrated. No explicit comparison across different boundary conditions (e.g., perfectly reflecting surface vs. finite-thickness shell) or effective potentials is referenced, which directly affects whether the discriminator is model-independent as asserted.

    Authors: The referee correctly identifies that the manuscript does not contain explicit numerical comparisons across multiple distinct mimicker models or boundary conditions. Our claim of genericity is grounded in the structure of the problem: the low-frequency comb arises at the real parts of the QNMs excited by the plunge, a feature expected for any mimicker possessing a reflective surface, while the high-frequency break occurs above a scale set by the light-ring frequency, which remains largely insensitive to interior details for objects whose surface lies close to the would-be horizon. To strengthen the presentation, we have added a paragraph in the conclusions elaborating on these theoretical reasons for expecting the features to hold across a broad class and noting that dedicated cross-model studies would be a natural extension. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on explicit model calculations rather than definitional reduction

full rationale

The paper computes plunge-induced spectra for specific black hole mimicker models, extracts the low-frequency QNM comb and the spectral break at Mω_th≈0.39 directly from the resulting waveforms or scattering amplitudes. These features are presented as outputs of the calculation for the chosen interior boundary conditions, not as inputs renamed as predictions. The genericity statement is an extrapolation from the model class examined, not a self-definitional loop or a fitted parameter called a prediction. No load-bearing step reduces to a prior self-citation or to an ansatz smuggled in; the derivation chain remains self-contained within the performed integrations and mode expansions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive identification; the numerical threshold and generic excitation assumption are the main unexamined inputs.

free parameters (1)
  • Mω_th
    Numerical threshold ≈0.39 for the spectral break; presented without derivation or error estimate in the abstract.
axioms (1)
  • domain assumption Plunge phase excites quasi-normal modes of the mimicker in a manner that produces observable spectral combs and breaks.
    Invoked to claim the two generic features without further justification in the provided abstract.

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Works this paper leans on

77 extracted references · 77 canonical work pages · 33 internal anchors

  1. [1]

    Plunge spectra as discriminators of black hole mimickers

    and others [22–24]. Such compact objects are difficult to distinguish from black holes observationally and could potentially ‘mimic’ a black hole. These black hole mimickers share the feature of perturbations propagating inwards not being completely absorbed, instead being reflected due to the absence of an event horizon. Detection of any such black hole ...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    We will start in Sec

    to enhance the signal-to-noise ratio (SNR) of GW events, suggests that despite the current difficulties with the SNR in the plunge phase of extreme mass ratio (EMR) events, the GW radiation during plunge could potentially become a powerful tool to identify black hole mimickers. We will start in Sec. II with an exploration of the the- oretical background o...

    work page

  3. [3]

    Resonances in the energy spectrum at low frequencies. For perturbation on a Schwarzschild background, the energy carried away to infinity through GW radiation per frequency can be expressed as dEℓm dω = ω2 64π2 (ℓ+ 2)! (ℓ−2)! C (+),out ℓmω 2 + 4 ω2 C (−),out ℓmω 2 . (11) Where,C (±),out ℓmω are the amplitudes of the outgoing modes of the solutionX (±) ℓmω...

    work page

  4. [4]

    (1), some- thing interesting happens whenM ω≳0.39

    New avenues at higher frequencies Let us begin by noticing that for the (ℓ, m) = (2,2) modes of the metric perturbations in Eq. (1), some- thing interesting happens whenM ω≳0.39. Above this, we will have the effective potential for the Zerilli modes to be less thanω 2, meaning that the perturbing frequencies can directly penetrate the near-horizon. 4 This...

    work page

  5. [5]

    Advanced LIGO

    J. Aasiet al.[LIGO Scientific],Advanced LIGO, Class. Quant. Grav.32, 074001 (2015), [arXiv:1411.4547 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  6. [6]

    Advanced Virgo: a 2nd generation interferometric gravitational wave detector

    F. Acerneseet al.[VIRGO],Advanced Virgo: a second-generation interferometric gravitational wave de- tector, Class. Quant. Grav.32, no.2, 024001 (2015), [arXiv:1408.3978 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    B. P. Abbottet al.[LIGO Scientific and Virgo],Ob- 10 servation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, no.6, 061102 (2016), [arXiv:1602.03837 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    B. P. Abbottet al.[LIGO Scientific and Virgo],GWTC- 1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X9, no.3, 031040 (2019), [arXiv:1811.12907 [astro-ph.HE]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  9. [9]

    GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run

    R. Abbottet al.[LIGO Scientific and Virgo],GWTC- 2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X11, 021053 (2021), [arXiv:2010.14527 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  10. [10]

    Akutsuet al.(KAGRA), Prog

    T. Akutsuet al.[KAGRA],Overview of KAGRA: Detec- tor design and construction history, PTEP2021, no.5, 05A101 (2021), [arXiv:2005.05574 [physics.ins-det]]

    work page arXiv 2021

  11. [11]

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

    R. Abbottet al.[KAGRA, VIRGO and LIGO Scien- tific],GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X13, no.4, 041039 (2023), [arXiv:2111.03606 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  12. [12]

    B. P. Abbottet al.[LIGO Scientific and Virgo],Tests of general relativity with GW150914, Phys. Rev. Lett.116, no.22, 221101 (2016) [erratum: Phys. Rev. Lett.121, no.12, 129902 (2018)], [arXiv:1602.03841 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  13. [13]

    B. P. Abbottet al.[LIGO Scientific and Virgo],Tests of General Relativity with GW170817, Phys. Rev. Lett. 123, no.1, 011102 (2019), [arXiv:1811.00364 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  14. [14]

    B. P. Abbottet al.[LIGO Scientific and Virgo],Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1, Phys. Rev. D 100, no.10, 104036 (2019), [arXiv:1903.04467 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  15. [15]

    Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog

    R. Abbottet al.[LIGO Scientific and Virgo],Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D103, no.12, 122002 (2021), [arXiv:2010.14529 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  16. [16]

    Tests of General Relativity with GWTC-3

    R. Abbottet al.[LIGO Scientific, VIRGO and KA- GRA],Tests of General Relativity with GWTC-3, [arXiv:2112.06861 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv

  17. [17]

    P. O. Mazur and E. Mottola,Gravitational condensate stars: An alternative to black holes,arXiv:gr-qc/0109035 [gr-qc]

    work page arXiv

  18. [18]

    Visser and D

    M. Visser and D. L. Wiltshire,Stable gravastars: An Al- ternative to black holes?, Class. Quant. Grav.21, 1135- 1152 (2004)

    work page 2004

  19. [19]

    Jetzer,Boson stars,Phys

    P. Jetzer,Boson stars,Phys. Rept.220, 163-227 (1992)

    work page 1992

  20. [20]

    F. E. Schunck and E. W. Mielke,General relativistic bo- son stars,Class. Quant. Grav.20, R301-R356 (2003)

    work page 2003

  21. [21]

    S. L. Liebling and C. Palenzuela,Dynamical Boson Stars, Living Rev. Rel.15, 6 (2012)

    work page 2012

  22. [22]

    J. D. Bekenstein,The quantum mass spectrum of the Kerr black hole,Lett. Nuovo Cim.11, 467 (1974)

    work page 1974

  23. [23]

    J. D. Bekenstein and V. F. Mukhanov,Spectroscopy of the quantum black hole,Phys. Lett. B360, 7-12 (1995)

    work page 1995

  24. [24]

    Ashtekar, J

    A. Ashtekar, J. Baez, A. Corichi and K. Krasnov,Quan- tum geometry and black hole entropy,Phys. Rev. Lett. 80, 904-907 (1998)

    work page 1998

  25. [25]

    S. D. Mathur,The Fuzzball proposal for black holes: An Elementary review,Fortsch. Phys.53(2005), 793-827 [arXiv:hep-th/0502050 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  26. [26]

    M. S. Morris, K. S. Thorne and U. Yurtsever,Wormholes, Time Machines, and the Weak Energy Condition,Phys. Rev. Lett.61(1988), 1446-1449

    work page 1988

  27. [27]

    Not quite a black hole

    B. Holdom and J. Ren,Not quite a black hole,Phys. Rev. D95(2017) no.8, 084034 [arXiv:1612.04889 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  28. [28]

    Anisotropic stars as ultracompact objects in General Relativity

    G. Raposo, P. Pani, M. Bezares, C. Palenzuela and V. Cardoso,Anisotropic stars as ultracompact objects in General Relativity,Phys. Rev. D99(2019) no.10, 104072 [arXiv:1811.07917 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  29. [29]

    Maggio, L

    E. Maggio, L. Buoninfante, A. Mazumdar and P. Pani, Phys. Rev. D102(2020) no.6, 064053 [arXiv:2006.14628 [gr-qc]]

    work page arXiv 2020

  30. [30]

    Laghi, G

    D. Laghi, G. Carullo, J. Veitch and W. Del Pozzo,Quan- tum black hole spectroscopy: probing the quantum nature of the black hole area using LIGO–Virgo ringdown detec- tions,Class. Quant. Grav.38, no.9, 095005 (2021)

    work page 2021

  31. [31]

    M. V. S. Saketh and E. Maggio,Quasinormal modes of slowly-spinning horizonless compact objects,Phys. Rev. D110(2024) no.8, 084038

    work page 2024

  32. [32]

    Cardoso, E

    V. Cardoso, E. Franzin, A. Maselli, P. Pani and G. Ra- poso,Testing strong-field gravity with tidal Love numbers, Phys. Rev. D95, no.8, 084014 (2017)

    work page 2017

  33. [33]

    S. Nair, S. Chakraborty and S. Sarkar,Dynamical Love numbers for area quantized black holes,Phys. Rev. D107 (2023) no.12, 124041 [arXiv:2208.06235 [gr-qc]]

    work page arXiv 2023

  34. [34]

    Chakraborty, E

    S. Chakraborty, E. Maggio, M. Silvestrini and P. Pani, Dynamical tidal Love numbers of Kerr-like compact objects,Phys. Rev. D110(2024) no.8, 084042 [arXiv:2310.06023 [gr-qc]]

    work page arXiv 2024

  35. [35]

    Berti, V

    E. Berti, V. De Luca, L. Del Grosso and P. Pani,Tidal Love numbers and approximate universal relations for fermion soliton stars,Phys. Rev. D109(2024) no.12, 124008 [arXiv:2404.06979 [gr-qc]]

    work page arXiv 2024

  36. [36]

    Silvestrini, E

    M. Silvestrini, E. Maggio, S. Chakraborty and P. Pani, One Membrane to Love them all: Tidal deforma- tions of compact objects from the membrane paradigm, [arXiv:2506.16516 [gr-qc]]

    work page arXiv

  37. [37]

    Tests for the existence of horizons through gravitational wave echoes

    V. Cardoso and P. Pani,Tests for the existence of black holes through gravitational wave echoes,Nature Astron. 1(2017) no.9, 586-591 [arXiv:1709.01525 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  38. [38]

    Z. Mark, A. Zimmerman, S. M. Du and Y. Chen,A recipe for echoes from exotic compact objects,Phys. Rev. D96 (2017) no.8, 084002 [arXiv:1706.06155 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  39. [39]

    Datta, R

    S. Datta, R. Brito, S. Bose, P. Pani and S. A. Hughes, Tidal heating as a discriminator for horizons in extreme mass ratio inspirals,Phys. Rev. D101(2020) no.4, 044004 [arXiv:1910.07841 [gr-qc]]

    work page arXiv 2020

  40. [40]

    L. F. Longo Micchi and C. Chirenti,Spicing up the recipe for echoes from exotic compact objects: orbital differences and corrections in rotating backgrounds,Phys. Rev. D 101(2020) no.8, 084010 [arXiv:1912.05419 [gr-qc]]

    work page arXiv 2020

  41. [41]

    Datta, Tidal heating of Quantum Black Holes and their imprints on gravitational waves, Phys

    S. Datta,Tidal heating of Quantum Black Holes and their imprints on gravitational waves,Phys. Rev. D102(2020) no.6, 064040 [arXiv:2002.04480 [gr-qc]]

    work page arXiv 2020

  42. [42]

    Agullo, V

    I. Agullo, V. Cardoso, A. D. Rio, M. Maggiore and J. Pullin,Potential Gravitational Wave Signatures of Quantum Gravity,Phys. Rev. Lett.126, no.4, 041302 (2021)

    work page 2021

  43. [43]

    Chakraborty, E

    S. Chakraborty, E. Maggio, A. Mazumdar and P. Pani, Implications of the quantum nature of the black hole hori- zon on the gravitational-wave ringdown,Phys. Rev. D 106, no.2, 024041 (2022)

    work page 2022

  44. [44]

    Chakravarti, R

    K. Chakravarti, R. Ghosh and S. Sarkar,Formation and stability of area quantized black holes,Phys. Rev. D109 (2024) no.4, 4 [arXiv:2310.18022 [gr-qc]]

    work page arXiv 2024

  45. [45]

    Datta, R

    S. Datta, R. Brito, S. A. Hughes, T. Klinger and P. Pani, Tidal heating as a discriminator for horizons in equato- 11 rial eccentric extreme mass ratio inspirals,Phys. Rev. D 110(2024) no.2, 024048 [arXiv:2404.04013 [gr-qc]]

    work page arXiv 2024

  46. [46]

    Black hole mimickers: from theory to observation,

    C. Bambi, R. Brustein, V. Cardoso, A. Chael, U. Daniels- son, S. Giri, A. Gupta, P. Heidmann, L. Lehner and S. Liebling,et al. Black hole mimickers: from theory to observation,[arXiv:2505.09014 [gr-qc]]

    work page arXiv

  47. [47]

    Cardoso, A

    V. Cardoso, A. del Rio and M. Kimura,Distinguishing black holes from horizonless objects through the excitation of resonances during inspiral,Phys. Rev. D100(2019), 084046 [erratum: Phys. Rev. D101(2020) no.6, 069902]

    work page 2019

  48. [48]

    Maggio, M

    E. Maggio, M. van de Meent and P. Pani,Extreme mass- ratio inspirals around a spinning horizonless compact ob- ject,Phys. Rev. D104(2021) no.10, 104026

    work page 2021

  49. [49]

    S. L. Detweiler,Black Holes and Gravitational Waves. I. Circular Orbits About a Rotating Hole,Astrophys. J. 225(1978), 687-693

    work page 1978

  50. [50]

    Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections

    E. Poisson and M. Sasaki,Gravitational radiation from a particle in circular orbit around a black hole. 5: Black hole absorption and tail corrections,Phys. Rev. D51 (1995), 5753-5767 [arXiv:gr-qc/9412027 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  51. [51]

    The Transition from Inspiral to Plunge for a Compact Body in a Circular Equatorial Orbit Around a Massive, Spinning Black Hole

    A. Ori and K. S. Thorne,The Transition from inspiral to plunge for a compact body in a circular equatorial orbit around a massive, spinning black hole,Phys. Rev. D62 (2000), 124022 [arXiv:gr-qc/0003032 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  52. [52]

    R. W. O’Shaughnessy,Transition from inspiral to plunge for eccentric equatorial Kerr orbits,Phys. Rev. D67 (2003), 044004 [arXiv:gr-qc/0211023 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  53. [53]

    P. A. Sundararajan,The Transition from adiabatic in- spiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits,Phys. Rev. D 77(2008), 124050 [arXiv:0803.4482 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  54. [54]

    Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole

    L. Barack and N. Sago,Gravitational self-force cor- rection to the innermost stable circular orbit of a Schwarzschild black hole,Phys. Rev. Lett.102(2009), 191101 [arXiv:0902.0573 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  55. [55]

    Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral

    S. Hadar and B. Kol,Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral,Phys. Rev. D84(2011), 044019 [arXiv:0911.3899 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  56. [56]

    Rom and R

    B. Rom and R. Sari,Extreme mass-ratio binary black hole merger: Characteristics of the test-particle limit,Phys. Rev. D106(2022) no.10, 104040 [arXiv:2204.11738 [gr- qc]]

    work page arXiv 2022

  57. [57]

    Binary black holes in the heat of merger

    S. Mukherjee, S. Datta, S. Bose and K. S. Phukon, [arXiv:2506.22363 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv

  58. [58]

    Laser Interferometer Space Antenna

    P. Amaro-Seoaneet al.[LISA],Laser Interferometer Space Antenna,[arXiv:1702.00786 [astro-ph.IM]]

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    K. G. Arunet al.[LISA],New horizons for fundamental physics with LISA,Living Rev. Rel.25(2022) no.1, 4 [arXiv:2205.01597 [gr-qc]]

    work page arXiv 2022

  60. [60]

    LISA Definition Study Report

    M. Colpiet al.[LISA],LISA Definition Study Report, [arXiv:2402.07571 [astro-ph.CO]]

    work page internal anchor Pith review Pith/arXiv arXiv

  61. [61]

    Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals

    S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sop- uerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Pe- titeau and A. Klein,Science with the space-based inter- ferometer LISA. V: Extreme mass-ratio inspirals,Phys. Rev. D95(2017) no.10, 103012 [arXiv:1703.09722 [gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  62. [62]

    H. Yang, K. Yagi, J. Blackman, L. Lehner, V. Pascha- lidis, F. Pretorius and N. Yunes,Black hole spectroscopy with coherent mode stacking,Phys. Rev. Lett.118(2017) no.16, 161101 [arXiv:1701.05808 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  63. [63]

    Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole

    V. Cardoso, J. P. S. Lemos and S. Yoshida,“Electro- magnetic radiation from collisions at almost the speed of light: An Extremely relativistic charged particle falling into a Schwarzschild black hole,”Phys. Rev. D68(2003), 084011 [arXiv:gr-qc/0307104 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  64. [65]

    Regge and J

    T. Regge and J. A. Wheeler,Stability of a Schwarzschild singularity,Phys. Rev.108(1957), 1063-1069

    work page 1957

  65. [66]

    F. J. Zerilli,Effective potential for even parity Regge- Wheeler gravitational perturbation equations,Phys. Rev. Lett.24(1970), 737-738

    work page 1970

  66. [67]

    F. J. Zerilli,Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D2(1970), 2141-2160

    work page 1970

  67. [68]

    Davis, R

    M. Davis, R. Ruffini, W. H. Press and R. H. Price,Grav- itational radiation from a particle falling radially into a schwarzschild black hole,Phys. Rev. Lett.27(1971), 1466-1469

    work page 1971

  68. [69]

    Tashiro and H

    Y. Tashiro and H. Ezawa,Gravitational Radiation of a Particle Falling Towards a Black Hole. I. The Case of Nonrotating Black Hole,Prog. Theor. Phys.66(1981), 1612-1626

    work page 1981

  69. [70]

    Shibata, T

    M. Shibata, T. Nakamura,Metric Perturbations Induced by a Particle Falling into a Schwarzschild Black Hole. I: Formulation, Progress of Theoretical Physics, Volume 87, Issue 5, (1992)

    work page 1992

  70. [71]

    N. Sago, H. Nakano and M. Sasaki,Gauge problem in the gravitational selfforce. 1. Harmonic gauge approach in the Schwarzschild background,Phys. Rev. D67(2003), 104017 [arXiv:gr-qc/0208060 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  71. [72]

    Semianalytical estimates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters

    E. Berti, V. Cardoso, T. Hinderer, M. Lemos, F. Pre- torius, U. Sperhake and N. Yunes,Semianalytical esti- mates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters,Phys. Rev. D 81(2010), 104048 [arXiv:1003.0812 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  72. [73]

    H. O. Silva, G. Tambalo, K. Glampedakis and K. Yagi, Gravitational radiation from a particle plunging into a Schwarzschild black hole: Frequency-domain and semirel- ativistic analyses,Phys. Rev. D109(2024) no.2, 024036 [arXiv:2308.14823 [gr-qc]]

    work page arXiv 2024

  73. [74]

    D. J. A. McKechan, C. Robinson and B. S. Sathyaprakash,A tapering window for time- domain templates and simulated signals in the detection of gravitational waves from coalescing compact binaries, Class. Quant. Grav.27(2010), 084020 [arXiv:1003.2939 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  74. [75]

    Y. Chen, M. Boyle, N. Deppe, L. E. Kidder, K. Mit- man, J. Moxon, K. C. Nelli, H. P. Pfeiffer, M. A. Scheel and W. Throwe,et al. Improved frequency spectra of gravitational waves with memory in a binary-black-hole simulation,Phys. Rev. D110(2024) no.6, 064049 [arXiv:2405.06197 [gr-qc]]

    work page arXiv 2024

  75. [76]

    R. F. Rosato, S. Biswas, S. Chakraborty and P. Pani, Greybody factors, reflectionless scattering modes, and echoes of ultracompact horizonless objects,Phys. Rev. D 111(2025) no.8, 084051 [arXiv:2501.16433 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  76. [77]

    Oshita, K

    N. Oshita, K. Takahashi and S. Mukohyama,Stability and instability of the black hole greybody factors and ring- downs against a small-bump correction,Phys. Rev. D 110(2024) no.8, 084070 [arXiv:2406.04525 [gr-qc]]

    work page arXiv 2024

  77. [78]

    R. F. Rosato, K. Destounis and P. Pani,Ringdown stability: Graybody factors as stable gravitational-wave observables,Phys. Rev. D110(2024) no.12, L121501 12 [arXiv:2406.01692 [gr-qc]]

    work page arXiv 2024